Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19097800 | C2 | semidirect |
| 3. C2×Q16×D157 | C2 | semidirect |
| 4. #23757843 | C2 | semidirect |
| 5. #23757668 | C2 | semidirect |
| 6. #23757664 | C2 | semidirect |
| 7. #23757656 | C2 | semidirect |
| 8. #23757653 | C2 | semidirect |
| 9. #23757651 | C2 | semidirect |
| 10. #23757227 | C2 | semidirect |
| 11. #495×C157 | C2 | semidirect |
| 121. C157 | #3156 | semidirect |
| 130. #495 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097800 | 2 |
| C2×#19097790 | 2 |
| C2×Q16×D157 | 2 |
| #23757843 | 2 |
| #23757668 | 2 |
| #23757664 | 2 |
| #23757656 | 2 |
| #23757653 | 2 |
| #23757651 | 2 |
| #23757227 | 2 |
| #495×C157 | 2 |
| #3156 | 157 |